Download Class 9 Mathematics Concept Summaries: CBSE Class 9 Mathematics Circles Notes Set 05
Review targeted revision notes for Class 9 Mathematics with the CBSE Class 9 Mathematics Circles Notes Set 05. Built according to official educational guidelines for the 2026-27 academic year, these downloadable summaries for Chapter 09 Circle support daily study and last-minute exam readiness.
Access Chapter 09 Circle Notes and Study Material
Navigate directly to the revision notes for Chapter 09 Circle using the digital viewer below. Each summary is structured to highlight high-weightage sections, allowing students to instantly access critical definitions and focus on core exam topics.
Basic Terms
A circle is the set of all points in a plane at a fixed distance (the radius) from a fixed point (the centre). A chord joins two points of the circle, and a diameter is the longest chord and passes through the centre. An arc is a part of the circle, and the angle it makes at the centre is its degree measure.
Circles with equal radii are congruent.
Chords and the Centre
| Result | Statement |
|---|---|
| 1 | Equal chords of a circle subtend equal angles at the centre, and the converse is true. |
| 2 | The perpendicular from the centre to a chord bisects the chord, and the line from the centre to the mid-point of a chord is perpendicular to it. |
| 3 | Equal chords are equidistant from the centre, and chords equidistant from the centre are equal. |
| 4 | One and only one circle passes through three non-collinear points. |
Useful calculation: if r is the radius, d the distance of a chord from the centre and c the chord length, then \( r^2 = d^2 + (c/2)^2 \). A larger chord is nearer to the centre.
Angles in a Circle
| Result | Statement |
|---|---|
| 1 | The angle subtended by an arc at the centre is double the angle it subtends at any point on the remaining part of the circle. |
| 2 | Angles in the same segment of a circle are equal. |
| 3 | The angle in a semicircle is a right angle. |
| 4 | If a line segment subtends equal angles at two points on the same side of it, the four points lie on a circle. |
Cyclic Quadrilaterals
A quadrilateral whose four vertices lie on a circle is cyclic. Its opposite angles add up to 180 degrees, and conversely, a quadrilateral with a pair of supplementary opposite angles is cyclic.
If one side of a cyclic quadrilateral is produced, the exterior angle equals the interior opposite angle. A cyclic parallelogram is a rectangle, and a cyclic trapezium is isosceles.
Intersecting Chords
If chords AB and CD intersect at P inside a circle, then \( PA \times PB = PC \times PD \). Equal arcs have equal chords and subtend equal angles at the centre.
Free study material for Mathematics
Study Material and Revision Notes for Class 9 Mathematics Chapter 09 Circle
Quick Revision Notes: Chapter 09 Circle (CBSE)
Explore reliable chapter overviews for Chapter 09 Circle tailored for Class 9 learners. Use these structured points to grasp difficult themes and ensure solid preparation for upcoming assessments.
Expert Study Material for Class 9 Mathematics
Each chapter summary is structured around standard CBSE textbooks, allowing students to check their understanding and clarify complex ideas early in their revision.
Complete Your Chapter Revision
Follow up your revision by attempting the interactive online Mathematics MCQ test and practice worksheets for this chapter to verify your mastery. All platform resources are free to access.
FAQs
You can download the teacher prepared revision notes for CBSE Class 9 Mathematics Circles Notes Set 05 from StudiesToday.com. These notes are designed as per 2026-27 academic session to help Class 9 students get the best study material for Mathematics.
Yes, our CBSE Class 9 Mathematics Circles Notes Set 05 include 50% competency-based questions with focus on core logic, keyword definitions, and the practical application of Mathematics principles which is important for getting more marks in 2026 CBSE exams.
Yes, our CBSE Class 9 Mathematics Circles Notes Set 05 provide a detailed, topic wise breakdown of the chapter. Fundamental definitions, complex numerical formulas and all topics of CBSE syllabus in Class 9 is covered.
These notes for Mathematics are organized into bullet points and easy-to-read charts. By using CBSE Class 9 Mathematics Circles Notes Set 05, Class 9 students fast revise formulas, key definitions before the exams.
No, all study resources on StudiesToday, including CBSE Class 9 Mathematics Circles Notes Set 05, are available for immediate free download. Class 9 Mathematics study material is available in PDF and can be downloaded on mobile.